Question 15
Find the equation (in terms of ) of the line through the points and
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Ask by Parsons Graham. in the United States

Mar 25,2025

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Question 15 Find the equation (in terms of $$ x $$ ) of the line through the points $$ (-2,-3) $$ and $$ (2,9) $$ Question Help: D Post to forum Submit Question

UpStudy AI · Accepted Answer

To find the equation of the line that passes through the points $$(-2, -3)$$ and $$(2, 9)$$, we can follow these steps:

1. **Calculate the slope (m)** of the line using the formula:
   $$
   m = \frac{y_2 - y_1}{x_2 - x_1}
   $$
   where $$(x_1, y_1) = (-2, -3)$$ and $$(x_2, y_2) = (2, 9)$$.

2. **Use the point-slope form** of the equation of a line:
   $$
   y - y_1 = m(x - x_1)
   $$
   We can choose either of the two points for $$(x_1, y_1)$$.

3. **Rearrange the equation** to get it in the slope-intercept form $$y = mx + b$$.

Let's start by calculating the slope $$m$$.

First, we will calculate $$m$$:

$$
m = \frac{9 - (-3)}{2 - (-2)} = \frac{9 + 3}{2 + 2} = \frac{12}{4} = 3
$$

Now, we can use the point-slope form with one of the points, say $$(-2, -3)$$:

$$
y - (-3) = 3(x - (-2))
$$

This simplifies to:

$$
y + 3 = 3(x + 2)
$$

Now, let's expand and rearrange this equation to find the equation in terms of $$x$$.

Expanding gives:

$$
y + 3 = 3x + 6
$$

Now, subtract 3 from both sides:

$$
y = 3x + 3
$$

Thus, the equation of the line in terms of $$x$$ is:

$$
y = 3x + 3
$$
The equation of the line is $$ y = 3x + 3 $$.

Question 15
Find the equation (in terms of ) of the line through the points and
Question Help: D Post to forum
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Question 15 Find the equation (in terms of ) of the line through the points and Question Help: D Post to forum Submit Question